Adaptive finite element relaxation schemes for hyperbolic conservation laws

Christos Arvanitis*, Theodoros Katsaounis, Charalambos Makridakis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar problems and the system of elastodynamics.

Original languageEnglish (US)
Pages (from-to)17-33
Number of pages17
JournalMathematical Modelling and Numerical Analysis
Volume35
Issue number1
DOIs
StatePublished - Jan 1 2001

Keywords

  • Adaptive methods
  • Conservation laws
  • Finite elements

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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